Report

Designing a High Resolution Fiber-Fed Spectrograph for Solar Observations Edmond Wilson Brennan Thomason Stephanie Inabnet Tamara Reed Harding University Project Goal Design a spreadsheet program to aid in optimizing the light throughput of a CzernyTurner Spectrograph fed by an optical fiber Czerny-Turner Monochromator Configuration http://terpconnect.umd.edu/~toh/models/Monochromator.png The model for our instrument is based on the discussion in Chapter 1 of the book, Guide for Spectroscopy, by Jobin Yvon/SPEX, 1994. Figure 1 below was created from Figure 3 in the book, with errors in the original figure corrected. Although the light path of a Czerny-Turner spectrometer is usually folded, mathematically, it can be treated as if the light path were arranged linearly without changing the results. Equivalent Optical Path for Czerny-Turner Spectrometer Begin with a grating…. Plane Grating Dimensions Richardson Grating Laboratories, Grating Model Number 290-R Enter Diffraction Order to Be Used in Calculations, k Enter height of grating in mm, hG Enter width of grating in mm, wG Enter thickness of grating in mm & inches Enter groove density of grating in grooves/mm, n Enter Blaze wavelength in Littrow configuration in nm Enter Nominal blaze angle in degrees Given 1 Given 58 Given 58 6 1800 500 26.7 Given Given Given Given Given Collimating Mirror Next Collimating Mirror Dimensions Enter parabolic mirror diameter in mm 64.00 Given 320.00 Given Parabolic mirror focal length in inches 12.60 Calculated Enter parabolic mirror edge thickness in mm 19.10 Given 5.00 Calculated Enter parabolic mirror focal length in mm Aperture, f/# (Calculated) Camera Camera Mirror Dimensions Enter parabolic mirror diameter in mm 64.00 Given 320.00 Given Parabolic mirror focal length in inches 12.60 Calculated Enter parabolic mirror edge thickness in mm 19.10 Given 5.00 Calculated Enter parabolic mirror focal length in mm Aperture, f/# (Calculated) Slit Parameters Slit Dimensions Enter Fixed Slit Height in mm, h 0.2987 Given Enter Fixed Slit Width in µm, w =bandpass/dispersion, mm 15 Given Spectral Bandpass desired, nm 0.5 Fiber Parameters Fiber Parameters Enter the diameter of the fiber in µm 1000 Given Enter numerical aperture of fiber 0.22 Given Length of Fiber Given Begin the Calculations Spectrometer Parameters Enter Dv in degrees Enter LA in mm (LA = F, Focal Length of Spectrometer) Grating Area in mm2 12.52 320.00 3364 Given Given Calculated αλ , value of α in degrees at the wavelength of interest 15.39 Calculated βλ , value of β in degrees at the wavelength of interest 39.39 Calculated f/# of spectrometer 5.00 Calculated NAs is the numerical aperture of the spectrometer f/# of fiber 0.1 2.5 Calculated Calculated NAf is the numerical aperture of the fiber 0.22 Given Complete Optical Path Optimization for a Czerny- Turner Spectrograph that Employs a Fiber Optic Cable to Supply Light to the Entrance Slit • Step 1. Calculate the entendue of the light source, G • = 2 where S = area of light source, mm2 and r = radius of fiber, mm • = 2 where G = geometric entendue, S = area of light source, NAf = numerical aperture of the fiber S= 7.85E-01 mm G= 1.19E-01 mm2 Step 2. Calculate the entendue, G, of the spectrometer Step 2a. Calculate the entendue of the spectrometer assuming a bandpass of 0.5 nm at 500 nm λ= 600nm Given BP = 0.5nm Given n= k= DV = 1800grooves/mm 1 Given Given 12.25Degrees Given 647.7mm Given 3364mm2 Calculated α600 = 15.39Degrees Calculated β600 = 39.39Degrees Calculated LA = F = L B = GA f/# spectrometer = 5.0 Calculated NAs = 0.1 Calculated f/# fiber = 2.3 Calculated NAf = 0.22 Given 3.00mm Given h= (G8 x G9) (G54) Calculate entrance slit width and area = 0.5829mm = 1.74879mm2 Calculate exit slit width 0.5829mm Finally, calculate G of the spectrometer 1.40E-02 spectrometer 1.19E-01 fiber Step 3. Re-image light from fiber to match it with the entendue of the monochromator so that the loss of photons and effect of stray light is minimized. This involves choosing Lens L1 in Figure 1. This is somewhat arbitrary. You must choose a focal length and diameter for lens L1 Diameter of Lens L1 in Figure 1 in mm 60 Focal length of Len L1 in Figure 1 in mm = 2 = 100 = 2 2 2 2 = Magnification, M = = =M M= 2.2 1 1 1 = + Solve for p and q (q = M x p) p= q= 145mm 320mm Solve for d, diameter of lens L1 d= 64mm Solve for d, diameter of Lens L1 d= 64mm # = 2 # = 2 1 = 1 = Solve for d, diameter of lens L1 d= 64mm Solve for d, diameter of Lens L1 d= 64mm Therefore, all the light from the fiber is collected by a lens, L1, with an object distance of p mm and will project an image of the fiber core on the spectrometer entrance slit q mm from lens, L1 Acknowledgement Thank you! Arkansas Space Grant Consortium Montana Space Grant Consortium